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1.
This paper presents the results of a non-adiabatic analysis for axisymmetric non-radial pulsations including the effect of a dipole magnetic field. Convection is assumed to be suppressed in the stellar envelope, and the diffusion approximation is used to radiative transport. As in a previous adiabatic analysis, the eigenfunctions are expanded in a series of spherical harmonics. The analysis is applied to a  1.9-M⊙  , main-sequence model  (log  T eff= 3.913)  . The presence of a magnetic field always stabilizes low-order acoustic modes. All the low-order modes of the model that are excited by the κ-mechanism in the He  ii ionization zone in the absence of a magnetic field are found to be stabilized if the polar strength of the dipole magnetic field is larger than about 1 kG. For high-order p modes, on the other hand, distorted dipole and quadrupole modes excited by the κ-mechanism in the H ionization zone remain overstable, even in the presence of a strong magnetic field. It is found, however, that all the distorted radial high-order modes are stabilized by the effect of the magnetic field. Thus, our non-adiabatic analysis suggests that distorted dipole modes and distorted quadrupole modes are most likely excited in rapidly oscillating Ap stars. The latitudinal amplitude dependence is found to be in reasonable agreement with the observationally determined one for HR 3831. Finally, the expected amplitude of magnetic perturbations at the surface is found to be very small.  相似文献   

2.
We consider both mode calculations and time-evolutions of axial r modes for relativistic uniformly rotating non-barotropic neutron stars, using the slow-rotation formalism, in which rotational corrections are considered up to linear order in the angular velocity Ω. We study various stellar models, such as uniform density models, polytropic models with different polytropic indices n , and some models based on realistic equations of state. For weakly relativistic uniform density models and polytropes with small values of n , we can recover the growth times predicted from Newtonian theory when standard multipole formulae for the gravitational radiation are used. However, for more compact models, we find that relativistic linear perturbation theory predicts a weakening of the instability compared to the Newtonian results. When turning to polytropic equations of state, we find that for certain ranges of the polytropic index n , the r mode disappears, and instead of a growth, the time-evolutions show a rapid decay of the amplitude. This is clearly at variance with the Newtonian predictions. It is, however, fully consistent with our previous results obtained in the low-frequency approximation.  相似文献   

3.
We present results of a comprehensive asteroseismic modelling of the β Cephei variable θ Ophiuchi. We call these studies complex asteroseismology because our goal is to reproduce both pulsational frequencies and corresponding values of a complex, non-adiabatic parameter, f , defined by the radiative flux perturbation. To this end, we apply the method of simultaneous determination of the spherical harmonic degree, ℓ, of excited pulsational mode and the corresponding non-adiabatic f parameter from combined multicolour photometry and radial velocity data. Using both the OP and OPAL opacity data, we find a family of seismic models which reproduce the radial and dipole centroid mode frequencies, as well as the f parameter associated with the radial mode. Adding the non-adiabatic parameter to seismic modelling of the B-type main-sequence pulsators yields very strong constraints on stellar opacities. In particular, only with one source of opacities it is possible to agree the empirical values of f with their theoretical counterparts. Our results for θ Oph point substantially to preference for the OPAL data.  相似文献   

4.
We study acoustic oscillations (eigenfrequencies, velocity distributions, damping times) of normal crusts of strange stars. These oscillations are very specific because of huge density jump at the interface between the normal crust and the strange matter core. The oscillation problem is shown to be self-similar. For a low (but non-zero) multipolarity l , the fundamental mode (without radial nodes) has a frequency of ∼300 Hz and mostly horizontal oscillation velocity; other pressure modes have frequencies ≳20 kHz and almost radial oscillation velocities. The latter modes are similar to radial oscillations (having approximately the same frequencies and radial velocity profiles). The oscillation spectrum of strange stars with crust differs from the spectrum of neutron stars. If detected, acoustic oscillations would allow one to discriminate between strange stars with crust and neutron stars and constrain the mass and radius of the star.  相似文献   

5.
A global analysis of the surface trapping of low-frequency non-radial g modes in rotating early-type stars is undertaken within the Cowling, adiabatic and traditional approximations. The dimensionless pulsation equations governing these modes are reviewed, and the boundary conditions necessary for solution of the equations are considered; in particular, an outer mechanical boundary condition, which does not enforce complete wave trapping at the stellar surface, is derived and discussed in detail. The pulsation equations are solved for a 7-M⊙ model star over a range of rotation rates, using a numerical approach.
The results of the calculations confirm the findings of the preceding paper in the series: modes with eigenfrequencies below a cut-off cannot be fully trapped within the star, and exhibit leakage in the form of outwardly propagating waves at the surface. The damping rates resulting from leakage are calculated for such 'virtual' modes, and found to be appreciably larger than typical growth rates associated with opacity-driven pulsation. Furthermore, it is demonstrated that the surface perturbations generated by virtual modes are significantly changed from those caused by fully trapped modes; the latter result suggests differences in the line-profile variations exhibited by these two types of mode.
The findings are discussed in the context of the 53 Per, SPB and pulsating Be classes of variable star. Whilst wave leakage will probably not occur for overstable g modes in the 53 Per and slowly rotating SPB stars, the adoption of the new outer mechanical boundary condition may still affect the pulsational stability of these systems. Wave leakage for overstable modes remains a possibility in Be stars and the more rapidly rotating SPB stars.  相似文献   

6.
The long-term monitoring and high photometric precision of the Kepler satellite will provide a unique opportunity to sound the stellar cycles of many solar-type stars using asteroseismology. This can be achieved by studying periodic changes in the amplitudes and frequencies of the oscillation modes observed in these stars. By comparing these measurements with conventional ground-based chromospheric activity indices, we can improve our understanding of the relationship between chromospheric changes and those taking place deep in the interior throughout the stellar activity cycle. In addition, asteroseismic measurements of the convection zone depth and differential rotation may help us determine whether stellar cycles are driven at the top or at the base of the convection zone. In this paper, we analyse the precision that will be possible using Kepler to measure stellar cycles, convection zone depths and differential rotation. Based on this analysis, we describe a strategy for selecting specific targets to be observed by the Kepler Asteroseismic Investigation for the full length of the mission, to optimize their suitability for probing stellar cycles in a wide variety of solar-type stars.  相似文献   

7.
The axial modes for non-barotropic relativistic rotating neutron stars with uniform angular velocity are studied, using the slow-rotation formalism together with the low-frequency approximation, first investigated by Kojima. The time-independent form of the equations leads to a singular eigenvalue problem, which admits a continuous spectrum. We show that for     , it is nevertheless also possible to find discrete mode solutions (the r modes). However, under certain conditions related to the equation of state and the compactness of the stellar model, the eigenfrequency lies inside the continuous band and the associated velocity perturbation is divergent; hence these solutions have to be discarded as being unphysical. We corroborate our results by explicitly integrating the time-dependent equations. For stellar models admitting a physical r-mode solution, it can indeed be excited by arbitrary initial data. For models admitting only an unphysical mode solution, the evolutions do not show any tendency to oscillate with the respective frequency. For higher values of l it seems that in certain cases there are no mode solutions at all.  相似文献   

8.
We undertook two time-series photometric multisite campaigns for the rapidly oscillating Ap star HD 122970. The first one, conducted in 1998, resulted in 119 h of data and in the detection of three pulsation frequencies. The presence of possible further modes which held the promise of deriving a mode identification motivated a second worldwide campaign in the year 2001. This second campaign resulted in 203 h of measurement, but did not reveal further modes. Rather, one of the previously detected signals disappeared. The two modes common to both data sets have different spherical degree. They also showed slight frequency modulation, and one of them varied in amplitude as well. Possible causes of the latter behaviour include intrinsic instability of the pulsation spectrum or precession of the pulsational axis and orbital motion in a binary system. Frequency analysis of the Hipparcos observations of the star did not allow us to determine the stellar rotation period. The amplitude and phase behaviour of the two modes of HD 122970 in the Strömgren uvby bands is quite similar to that observed for other roAp stars.  相似文献   

9.
The amplitude of solar-like oscillations results from a balance between excitation and damping. As in the sun, the excitation is attributed to turbulent motions that stochastically excite thep modes in the uppermost part of the convective zone. We present here a model for the excitation mechanism. Comparisons between modeled amplitudes and helio and stellar seismic constraints are presented and the discrepancies discussed. Finally the possibility and the interest of detecting such stochastically excited modes in pre-main sequence stars are also discussed.  相似文献   

10.
熊大闰  邓李才 《天文学报》2006,47(3):256-267
利用一种非定常的恒星非局部对流理论,对球状星团中低光度的红巨星进行了线性非绝热脉动理论计算．结果表明,对所有温度高于约5400 K模型的基音到4阶泛音都是脉动稳定的．随着恒星光度的增大,低阶泛音也变得脉动不稳定．对中低光度的红巨星,脉动稳定性非常低,接近中性稳定．因此他们将是不变星或非常小振幅的短周期变星(P<2天)．  相似文献   

11.
Using our non-local time-dependent theory of convection, the linear non-adiabatic oscillations of 10 evolutionary model series with masses of  1–3 M⊙  are calculated. The results show that there is a red giant instability strip in the lower temperature side of the Hertzsprung–Russell diagram which goes along the sequences of the red giant branch and the asymptotic giant branch. For red giants of lower luminosities, pulsation instability is found at high order overtones; the lower order modes from the fundamental to the second overtone are stable. Towards higher luminosity and lower effective temperature, instability moves to lower order modes, and the amplitude growth rate of oscillations also grows. At the high luminosity end of the strip, the fundamental and the first overtone become unstable, while all the modes above the fourth order become stable. The excitation mechanisms have been studied in detail. It is found that turbulent pressure plays a key role for excitation of red variables. The frozen convection approximation is unavailable for the low temperature stars with extended convective envelopes. In any case, this approximation can explain neither the red edge of the Cepheid instability strip, nor the blue edge of the pulsating red giant instability strip. An analytic expression of a pulsation constant as a function of stellar mass, luminosity and effective temperature is presented from this work.  相似文献   

12.
Photometric and Doppler imaging observations of active binaries indicate the existence of starspots at preferred longitudes (position angles with respect to the companion star). We investigate the stability of magnetic flux tubes in the convection zone of close, fast‐rotating binary stars and explore whether the observed preferred longitudes could be caused by tidal forces and the deformation of the active star. We assume a synchronized binary system with spin axes perpendicular to the orbital plane and a rotation period of a few days. The tidal force and the deviation from spherical structure are considered in lowest‐order perturbation theory. The magnetic field is in the form of toroidal magnetic flux rings, which are stored in mechanical equilibrium within the stably stratified overshoot region beneath the convection zone until the field has grown sufficiently strong for the undulatory instability to initiate the formation of rising loops. Frequencies and geometry of stable as well as growth rates of unstable eigenmodes are determined by linear stability analysis. Particular consideration is given to the question whether the effects of tidal forces and perturbations of the stellar structure can force a rising flux loop to enter the convection zone at specific longitudes.  相似文献   

13.
The systematic patterns of separations between frequencies of modes of different degree and order are a characteristic of p-mode oscillations of stars. The frequency separations depend on the internal structure of the star and so measuring them in the observed oscillation spectra of variable stars gives valuable diagnostics of the interior of a star. Roxburgh & Vorontsov proposed using the ratio of the so-called small frequency separation to the large frequency separation as a diagnostic of the stellar interior, and demonstrated that this ratio was less sensitive than the individual frequency separations themselves to uncertain details of the near-surface structure. Here we derive kernels relating the frequency separation ratio to structure, and show why the ratio is relatively insensitive to the near-surface structure in terms of the very small amplitude of the kernels in the near-surface layers. We also investigate the behaviour of the separation ratio for stars of different masses and ages, and demonstrate the usefulness of the ratio in the so-called asteroseismic Hertzsprung–Russell diagram.  相似文献   

14.
1 INTRODUCTIONThe mixing length theory (MLT) for stellar convection originally developed by Vitense(1953, 1958) has been the most popularly used local convection theory in the studies of stellarstructure and evolution. The theory was later modified and revised by many investigators,who suggested some different expressions. In fact, MLT is not a real hydrodynamic theory,rather, it is a simple "ballistic" theory which traces the motion of imaginary convective elements. In reality j stell…  相似文献   

15.
Recent ROSAT measurements show that the X-ray emission from isolated neutron stars is modulated at the stellar rotation period. To interpret these measurements, one needs precise calculations of the heat transfer through the thin insulating envelopes of neutron stars. We present nearly analytic models of the thermal structure of the envelopes of ultramagnetized neutron stars. Specifically, we examine the limit in which only the ground Landau level is filled. We use the models to estimate the amplitude of modulation expected from non-uniformities in the surface temperatures of strongly magnetized neutron stars. In addition, we estimate cooling rates for stars with fields B  ∼ 1015 − 1016 G, which are relevant to models that invoke 'magnetars' to account for soft γ-ray emission from some repeating sources.  相似文献   

16.
p-mode oscillations in solar-like stars are excited by the outer convection zone in these stars and reflected close to the surface. The p modes are trapped inside an acoustic cavity, but the modes only stay trapped up to a given frequency [known as the acoustic cut-off frequency  (νac)  ] as modes with larger frequencies are generally not reflected at the surface. This means that modes with frequency larger than the acoustic cut-off frequency must be travelling waves. The high-frequency modes may provide information about the physics in the outer layers of the stars and the excitation source and are therefore highly interesting as it is the estimation of these two phenomena that cause some of the largest uncertainties when calculating stellar oscillations.
High-frequency modes have been detected in the Sun, in β Hydri and in α Cen A and α Cen B by smoothing the so-called echelle diagram and the large frequency separation as a function of frequency has been estimated. The large frequency separation has been compared with a simple model of the acoustic cavity which suggests that the reflectivity of the photosphere is larger at high frequency than predicted by standard models of the solar atmosphere and that the depth of the excitation source is larger than what has been estimated by other models and might depend on the order n and degree l of the modes.  相似文献   

17.
The α Centauri (α Cen) binary system is a well-known stellar system with very accurate observational constraints on the structure of its component stars. In addition to the classical non-seismic constraints, there are also seismic constraints for the interior models of α Cen A and B. These two types of constraint give very different values for the age of the system. While we obtain 8.9 Gyr for the age of the system from the non-seismic constraints, the seismic constraints imply that the age is about 5.6–5.9 Gyr. There may be observational or theoretical reasons for this discrepancy, which can be found by careful consideration of similar stars. The α Cen binary system, with its solar-type components, is also suitable for testing the stellar mass dependence of the mixing-length parameter for convection derived from the binaries of Hyades. The values of the mixing-length parameter for α Cen A and B are 2.10 and 1.90 for the non-seismic constraints. If we prioritize the seismic constraints, we obtain 1.64 and 1.91 for α Cen A and B, respectively. By taking into account these two contrasting cases for stellar mass dependence of the mixing-length parameter, we derive two expressions for its time dependence, which are also compatible with the mass dependence of the mixing-length parameter derived from the Hyades stars. For assessment, these expressions should be tested in other stellar systems and clusters.  相似文献   

18.
The first results of numerical analysis of classical r-modes of rapidly rotating compressible stellar models are reported. The full set of linear perturbation equations of rotating stars in Newtonian gravity is solved numerically without the slow rotation approximation. A critical curve of gravitational wave emission induced instability, which restricts the rotational frequencies of hot young neutron stars, is obtained. Taking the standard cooling mechanisms of neutron stars into account, we also show the 'evolutionary curves' along which neutron stars are supposed to evolve as cooling and spinning down proceed. Rotational frequencies of 1.4-M⊙ stars suffering from this instability decrease to around 100 Hz when the standard cooling mechanism of neutron stars is employed. This result confirms the results of other authors, who adopted the slow rotation approximation.  相似文献   

19.
We apply for the first time the time-dependent convection (TDC) treatment of Gabriel and Grigahcène et al. to the photometric mode identification in γ Doradus (γ Dor) stars. We consider the influence of this treatment on the theoretical amplitude ratios and phase differences. Comparison with the observed amplitudes and phases of the stars γ Dor, 9 Aurigae, HD 207223 = HR 8330, HD 12901 and 48501 is presented and enables us to identify the degree ℓ of the pulsation modes for four of them. We also determine the mode stability for different models of these stars. We show that our TDC models agree better with observations than with frozen convection models. Finally, we compare the results obtained with different values of the mixing-length parameter α.  相似文献   

20.
We continue the study of the properties of non-radial pulsations of strange dwarfs. These stars are essentially white dwarfs with a strange quark matter (SQM) core. We have previously shown that the spectrum of oscillations should be formed by several, well-detached clusters of modes inside which the modes are almost evenly spaced. Here, we study the relation between the characteristics of these clusters and the size of the SQM core. We do so assuming that, for a given cluster, the kinetic energy of the modes is constant. For a constant amplitude of the oscillation at the stellar surface, we find that the kinetic energy of the modes is very similar for the cases of models with Log Q SQM=−2, −3 and −4, while it is somewhat lower for  Log Q SQM=−5  (here   Q SQM≡ M SQM/ M ; M SQM  and M are the masses of the SQM core and the star, respectively). Remarkably, the shape (amplitude of the modes versus period of oscillation) of the clusters of periods is very similar. However, the number of modes inside each cluster is strongly (and non-monotonously) dependent upon the size of the SQM core.
The characteristics of the spectrum of oscillations of strange dwarf stars are very different from the ones corresponding to normal white dwarfs and should be, in principle, observable. Consequently, the stars usually considered as white dwarfs may indeed provide an interesting and affordable way to detect SQM in an astrophysical environment.  相似文献   

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